Some floppy backbands can be dangerous because it gets in the way and inhibits reentries in self and assisted rescues. Sometimes it can be fixed by securing a bungee line from the center back of the band to the back coaming ( requires drilling a hole in the coaming lip). Personnaly, I’ve come to like built up minicell back rest, or a wide center pillar that reaches past the coaming to touch and support your lower back. No higher than the back coaming and shaped on top to facilitate layback rolls.
Tony if you get down this way with that kayak I have plenty of the grey closed cell foam and can show you how I made the type of back support that Sing mentioned. I would be glad to let you make one from what I have one hand.
I’ve had the same problem (floppy seat backs) with several of the used kayaks I’ve accumulated over the years. I have found that the fatter pool noodles (I think they are 4 or 5") work really well if you cut about a 24" to 30" length and shove them tightly under the lip of the cockpit back. Depending on the seat back or backband design, it can wedge it in place and even make it more comfortable. Only drawback is losing that space behind the seat for stashing water bottles or other small items. If the distance behind the seat to the stern bulkhead is too deep, you can add a couple of the standard skinny pool noodle chunks behind it. Also slicing the thick noodles in half lengthwise (serrated steak knives work great for this) can create pieces that help to fill in the space. These sliced pieces also work well for creating thigh brace surfaces in a too-large cockpit.
You do have to remember to watch for “escaped” pool noodle bits if you don’t tether them somehow. I run paracord through the hollow ones and wrap short bungees around the solid ones so they can be secured. The 3 I have stashed behind the wobbly seat back in my salvaged Avatar kayak (two skinny ones and a fat one) are duct-taped together and wedged so tight they don’t pop out easily.